Numerical aptitude · Numbers
Squares, cubes and roots, made easy
💡 The idea
A square number is a square of tiles: 5 rows of 5 = 25. The square root goes backwards: 25 tiles in a square → each side is 5.
🧭 The method: 3 steps
- Learn the squares up to 30 and cubes up to 10: they come up all the time.
- For a root, look at the last digit to guess the last digit of the answer, then find the nearest square you know.
- Near 50 or 100? Use (100 − a)² = 10000 − 200a + a².
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. √576?
- 20² = 400, 30² = 900, so it is in the 20s
- 576 ends in 6 → the root ends in 4 or 6
- 24² = 576 ✔
Example 2. 97²?
- 97 = 100 − 3
- 10000 − 600 + 9
- = 9409
Example 3. √(9/16)?
- Root of the top: 3
- Root of the bottom: 4
- = 3/4
⚠️ Where people go wrong
- A square root is NOT half (√36 is 6, not 18).
- (a − b)² is not a² − b²: do not forget the middle part.
- Cube root is not ÷ 3.
📌 Remember
- 1² … 30²
- 2³=8, 3³=27, 4³=64, 5³=125
- Last digit 6 → root ends in 4 or 6